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Maths-

General

Easy

Question

A system of two linear equations has no solutions. The graph of one of the equations in the system is shown in the xy - plane.

The second equation in the system is $a x minus y equals 1$ , where a is a constant. What is the value of a ?

The correct answer is: 1.25

Step 1 :- find the slope of line passing through points (0,4) and (-4,-1)
Slope m for the line passing through (x₁ ,y₁) and (x₂ ,y₂) is
m = $fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction not stretchy rightwards double arrow m equals fraction numerator negative 1 minus 4 over denominator 0 minus left parenthesis negative 4 right parenthesis end fraction equals 5 over 4$
Step 2 : finding slope of equation $a x minus y equals 1$
$y equals a x minus 1$ it is in the form of slope-intercept form of line
So, slope = a and y intercept = -1( which is different from shown line)
The two lines are not overlapping .so, the infinite no.of solutions condition is avoided.
Both slopes are equal so a = $5 over 4$ (or) 1.25

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